Sure, pure mathematical theory has a tendency to become useful later, but finding specific Mersenne primes is not pure math.
It’s not known if there is an infinite number of Mersenne primes (though it is strongly suspected) - so an interesting mathematical object to discover would be ‘the largest Mersenne prime’ - but this process isn’t going to find that (it might find a candidate but it won’t find a proof). If there are indeed infinite Mersennes then this search is just guaranteed to keep finding more forever.
It’s like looking for green pebbles on a beach. It’s nice when you find one to add to your collection, but it’s not that surprising, and if you keep looking you’ll probably find more. You’re not advancing geological knowledge if you keep looking and finding more.